Question

A ski resort claims that there is a 75% chance of snow on any given day in January and that snowfall happens independently from one day to the next. A family plans a four-day trip to this ski resort in January. Let X represent the number of days it snows while the family is there. What are the mean and standard deviation of X?

Option Choices:

Answer 1

Answer:

Its D

Step-by-step explanation:

Answer 2

Using the binomial distribution, it is found that the mean and the standard deviation of X are given as follows:

$\mu_X = 3, \sigma_X = 0.87$

What is the binomial probability distribution?

The expected value of the binomial distribution is:

$\mu_X = np$

The standard deviation of the binomial distribution is:

$\sigma_X = \sqrt{np(1-p)}$

In this problem, the proportion and the sample size are given as follows:

• p = 0.75.

• n = 4.

Hence, the mean and the standard deviation are given by:

$\mu_X = np = 4(0.75) = 3$

$\sigma_X = \sqrt{np(1-p)} = \sqrt{4(0.75)(0.25)} = 0.87$

More can be learned about the binomial distribution at https://brainly.com/question/24863377

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